A062178 a(n+1) = 2a(n)-a([n/2]) starting with a(0)=0 and a(1)=1.

0, 1, 2, 3, 5, 8, 14, 25, 47, 89, 173, 338, 668, 1322, 2630, 5235, 10445, 20843, 41639, 83189, 166289, 332405, 664637, 1328936, 2657534, 5314400, 10628132, 21254942, 42508562, 85014494, 170026358, 340047481, 680089727, 1360169009, 2720327573

Offset: 0

Author

Henry Bottomley, Jun 12 2001

Keywords

• nonn

Comments

As partial sum of Narayana-Zidek-Capell numbers A002083, this is the number of words beginning with 1, with sum of integers <=n, in the sequence 1, 11, 111, 112, 1111, 1112, 1113, 1121, 1122, 1123, 1124, 11111, 11112, 11113, 11114, 11121, 11122, 11123, 11124, 11125, 11131, 11132, 11133, 11134, 11135, 11136, where any positive integer, in any word, is <= the sum of the preceding integers.

The subsequence of primes in this partial sum begins: 2, 3, 5, 47, 89, 173, 166289. [From Jonathan Vos Post, Feb 17 2010]

For n > 0: a(n) = A005255(n-1) + 1. - Reinhard Zumkeller, Nov 18 2012

Examples

			a(7)=2a(6)-a(3)=2*14-3=25. a(8)=2a(7)-a(3)=2*25-3=47. a(9)=2a(8)-a(4)=2*47-5=89.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Programs

Haskell

a062178 n = a062178_list !! (n-1)
a062178_list = scanl (+) 0 a002083_list
-- Reinhard Zumkeller, Nov 18 2012

Formula

a(n) =a(n-1)+A002083(n).